Zobrazeno 1 - 10
of 173
pro vyhledávání: '"Thorne, Jack A."'
Autor:
Romano, Beth, Thorne, Jack A.
We give a generalisation of the Lenstra-Lenstra-Lov\'asz (LLL) lattice-reduction algorithm that is valid for an arbitrary (split, semisimple) reductive group $G$. This can be regarded as `lattice reduction with symmetries'. We make this algorithm exp
Externí odkaz:
http://arxiv.org/abs/2408.07012
Autor:
Laga, Jef, Thorne, Jack A.
We study the universal family of odd hyperelliptic curves of genus $g \geq 1$ over $\mathbb{Q}$. We relate the heights of $\mathbb{Q}$-points of Jacobians of curves in this family to the reduction theory of the representation of $\mathrm{SO}_{2g+1}$
Externí odkaz:
http://arxiv.org/abs/2405.10224
Autor:
Thorne, Jack A.
We define a reduction covariant for the representations a la Vinberg associated to stably graded Lie algebras. We then give an analogue of the LLL algorithm for the odd split special orthogonal group and show how this can be combined with our theory
Externí odkaz:
http://arxiv.org/abs/2405.10217
Let $f$ be a non-CM Hecke eigenform of weight $k \geq 2$. We give a new proof of some cases of Langlands functoriality for the automorphic representation $\pi$ associated to $f$. More precisely, we prove the existence of the base change lifting, with
Externí odkaz:
http://arxiv.org/abs/2312.01774
We prove the Ramanujan and Sato-Tate conjectures for Bianchi modular forms of weight at least 2. More generally, we prove these conjectures for all regular algebraic cuspidal automorphic representations of $\mathrm{GL}_2(\mathbf{A}_F)$ of parallel we
Externí odkaz:
http://arxiv.org/abs/2309.15880
Autor:
Newton, James, Thorne, Jack A.
Let $F$ be a totally real field. We prove the existence of all symmetric power liftings of those cuspidal automorphic representations of $\mathrm{GL}_2(\mathbf{A}_F)$ associated to Hilbert modular forms of regular weight.
Externí odkaz:
http://arxiv.org/abs/2212.03595
Autor:
Thorne, Jack A.
We construct level-raising congruences between $p$-ordinary automorphic representations, and apply this to the problem of symmetric power functoriality for Hilbert modular forms. In particular, we prove the existence of the $n^\text{th}$ symmetric po
Externí odkaz:
http://arxiv.org/abs/2212.03591
Autor:
Thorne, Jack A.
Let $\rho$ be the $p$-adic Galois representation attached to a cuspidal, regular algebraic, polarizable automorphic representation of $GL_n$. Assuming only that $\rho$ satisfies an irreducibility condition, we prove the vanishing of the adjoint Bloch
Externí odkaz:
http://arxiv.org/abs/2207.04925
Publikováno v:
Compositio Math. 160 (2024) 1959-2004
Let $G$ be a split semi-simple group over a global function field $K$. Given a cuspidal automorphic representation $\Pi$ of $G$ satisfying a technical hypothesis, we prove that for almost all primes $\ell$, there is a cyclic base change lifting of $\
Externí odkaz:
http://arxiv.org/abs/2205.04499
Autor:
Miagkov, Konstantin, Thorne, Jack A.
Let $F$ be a CM number field. We generalize existing automorphy lifting theorems for regular residually irreducible $p$-adic Galois representations over $F$ by relaxing the big image assumption on the residual representation.
Externí odkaz:
http://arxiv.org/abs/2203.04520